A novel approach to elucidation of cosmic star formation history is a blind search for CO and [CII] emissions using a ultra-wide-band imaging spectrograph on the future large submm telescopes like AtLAST and LST. In particular, searching for [CII] emitters in the appropriate frequency range allows us to sample those sources very efficiently for a redshift range of 3.5 to 9 (190 to 420 GHz), reaching the star-formation in the EoR. Further, spectroscopic analysis of CO in the lower frequency bands will constrain the evolution of CO luminosity functions across cosmic time. We conducted a feasibility study of ``CO/[CII] tomography'' based on a mock galaxy catalog containing 1.4 million objects drawn from the S$^3$-SAX (Obreschkow et al.~2009). We find that a blind spectroscopic survey using a 50-m telescope equipped with a 100-pixel imaging spectrograph, which covers 70--370 GHz simultaneously, will be promising indeed. A survey of 2 deg$^2$ in 1,000 hr (on-source) will uncover > 10^5 line-emitting galaxies in total, including ~10^3 [CII] emitters in the EoR (Tamura et al., in prep.). Wider surveys (10 deg^2 or wider) will also be discussed for RSD science cases.